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|
/*@@
@file AHFinder_flow.F
@date November 1998
@author Miguel Alcubierre
@desc
Master routine to control the iterations for
the flow algorithm.
The flow algorithm used here is that of Carsten Gunlach:
Phys. Rev. D 57, 863 (1998).
@enddesc
@@*/
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
subroutine AHFinder_flow(CCTK_ARGUMENTS,rmx,status,logf)
use AHFinder_dat
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
logical status,new,update
integer i,j,l,m
integer itmax
CCTK_REAL rmx,ahftol
CCTK_REAL A,B
CCTK_REAL ahfsum,ahfdiff,ahfdiff_old
CCTK_REAL reldiff
CCTK_REAL maxchange,minchange
CCTK_REAL zero,one
CCTK_REAL dd,aux
character(len=200) :: logf
! Description of variables:
!
! new Flag to indicate that stepsize has changed.
! update Flag to indicate if coefficients will be updated.
!
! i,j,l,m Counters.
!
! itmax Maximum number of iterations.
!
! ahftol Tolerance used to decide if we have converged.
!
! A,B Flow parameters.
!
! hw Weigth of `H' flow (see Carsten's paper).
! cw Weigth of `C' flow (see Carsten's paper).
! nw Weigth of `N' flow (see Carsten's paper).
!
! ahfsum Square root of the sum of the squares of the
! expansion coefficients.
!
! ahfdiff Square root of the sum of the squares of the
! change in the coefficients.
!
! rediff Relative difference between having done one large
! step and two small ones.
!
! maxchange A value of "reldiff" larger than this forces a
! reduction of the stepsize.
!
! minchange A value of "reldiff" smaller than this forces an
! increase of the stepsize.
!
! dd Maximum of (dx,dy,dz).
! ***************************
! *** DEFINE NUMBERS ***
! ***************************
zero = 0.0D0
one = 1.0D0
dd = max(dx,dy,dz)
! ***************************
! *** FIND PARAMETERS ***
! ***************************
A = ahf_flowa
B = ahf_flowb
hw = ahf_flowh
cw = ahf_flowc
nw = ahf_flown
maxchange = ahf_maxchange
minchange = ahf_minchange
! *******************************
! *** MAIN ITERATION LOOP ***
! *******************************
! Find itmax and ahftol.
itmax = ahf_flowiter
ahftol = ahf_flowtol
! Start the iterations.
do i=1,itmax
! Save the old values of the coefficients.
c0_old = c0
cc_old = cc
cs_old = cs
! In order to adapt the stepsize, I do two steps
! with the current stepsize, and compare them with
! one step with double the stepsize.
do j=1,2
ahfsum = zero
ahfdiff = zero
! ************************************
! *** FIND SPECTRAL COMPONENTS ***
! ************************************
call AHFinder_fun(CCTK_ARGUMENTS)
call AHFinder_exp(CCTK_ARGUMENTS)
call AHFinder_int(CCTK_ARGUMENTS)
! *****************************
! *** CHECK ERROR FLAGS ***
! *****************************
update = .true.
! If interror is true there was an error in the integral.
! There are two possibilities here:
! 1) This is the first of the two small steps (j=1).
! We then went out of bounds in the previous iteration,
! so there is nothing we can do to fix it.
if (interror.and.(j.eq.1)) then
! We can be out of bounds for three reasons:
! a) The radius is negative somewhere. This can mean
! one of two things:
!
! * There is no horizon, and the flow has reached
! the origin.
!
! * The origin for our expansion is outside the horizon.
! This can happen if the black-hole is not centered,
! or if we have more than one horizon.
if (interror1.ne.0) then
write(*,*)
write(*,*) 'Negative radius.'
return
! b) We are out of the computational domain, pity.
else if (interror2.ne.0) then
write(*,*)
write(*,*) 'Out of bounds, giving up.'
return
! c) We are inside the mask.
else if (interror3.ne.0) then
write(*,*)
write(*,*) 'Inside mask, giving up.'
return
! We should never get here!
else
write(*,*)
write(*,*) 'PANIC! Something is very wrong.'
return
end if
! 2) This is the second of the two small steps (j=2).
! We can still try to reduce the stepsize and start
! the iteration again. We then return the coefficients
! to their original values and, and do not update them.
!
! Since I will not update the coefficients, I need to
! assign values to "afhsum" and "ahfdiff". In order
! to force a reduction of the step size, I assign
! a very large number to "ahfdiff", which will make
! "reldiff" close to 1.0, far too large. I also
! assign a value of 1.0 to "ahfsum", so it is much
! smaller than "ahfdiff". This is important in order
! to prevent the algorithm from thinking we are done
! (see below for termination criteria).
else if (interror) then
interror = .false.
c0 = c0_old
cc = cc_old
cs = cs_old
ahfsum = one
ahfdiff = 1.0D10
update = .false.
end if
! ****************************************
! *** UPDATE SPECTRAL COEFFICIENTS ***
! ****************************************
if (update) then
! Update c0.
do l=0,lmax,1+stepz
aux = c0(l)
c0(l) = aux - A/(one + B*dble(l)*(dble(l) + one))
. *(hw*hflow0(l) + cw*cflow0(l) + nw*nflow0(l))
ahfsum = ahfsum + c0_old(l)**2
ahfdiff = ahfdiff + (c0(l) - c0_old(l))**2
end do
! Update {cc,cs}.
if (nonaxi) then
! Update cc(l,m).
do l=1,lmax
do m=1+stepx,l,1+stepx
if (stepz*mod(l-m,2).eq.0) then
aux = cc(l,m)
cc(l,m) = aux - A/(one
. + B*dble(l)*(dble(l) + one))
. *(hw*hflowc(l,m) + cw*cflowc(l,m)
. + nw*nflowc(l,m))
ahfsum = ahfsum + cc_old(l,m)**2
ahfdiff = ahfdiff + (cc(l,m)-cc_old(l,m))**2
end if
end do
end do
! Update cs(l,m).
if (.not.refy) then
do l=1,lmax
do m=1,l,1+stepx
if (stepz*mod(l-m,2).eq.0) then
cs(l,m) = cs(l,m) - A/(one
. + B*dble(l)*(dble(l) + one))
. *(hw*hflows(l,m) + cw*cflows(l,m)
. + nw*nflows(l,m))
ahfsum = ahfsum + cs_old(l,m)**2
ahfdiff = ahfdiff + (cs(l,m)-cs_old(l,m))**2
end if
end do
end do
end if
end if
ahfsum = sqrt(ahfsum)
ahfdiff = sqrt(ahfdiff)
! If this is the first of the two small steps, save
! twice the difference. Why twice? Because this would
! have been the resulting difference if we had done only
! one step that was twice as big.
if (j.eq.1) then
ahfdiff_old = 2.0D0*ahfdiff
end if
end if
end do
! ************************************
! *** FIND RELATIVE DIFFERENCE ***
! ************************************
! Here we find the relative difference between having done two
! small steps and one large step.
reldiff = abs(ahfdiff - ahfdiff_old)
. / (abs(ahfdiff) + abs(ahfdiff_old))
! Open logfile.
logf = filestr(1:nfile)//"/ahf_logfile"
if (logfile.and.(myproc.eq.0)) then
open(11,file=logf,form='formatted',status='old',
. position='append')
end if
! ***************************
! *** ADJUST STEPSIZE ***
! ***************************
new = .false.
! If the relative difference is too large, we reduce the
! stepsize for the next iteration.
if ((reldiff.gt.maxchange).or.
. (ahfdiff.gt.maxchange*ahfsum)) then
new = .true.
A = 0.5D0*A
if (veryver) then
write(*,*)
write(*,"(A15,ES14.6)") ' New stepsize =',A
end if
if (logfile) then
write(11,*)
write(11,"(A15,ES14.6)") ' New stepsize =',A
end if
! If the difference is too small, we can safely increase
! the stepsize for the next iteration.
else if (reldiff.lt.minchange) then
new = .true.
A = 2.0D0*A
if (veryver) then
write(*,*)
write(*,"(A15,ES14.6)") ' New stepsize =',A
end if
if (logfile) then
write(11,*)
write(11,"(A15,ES14.6)") ' New stepsize =',A
end if
end if
! ******************************************
! *** LOGFILE AND MESSAGES TO SCREEN ***
! ******************************************
! Write messages.
if (myproc.eq.0) then
if (veryver) then
write(*,*)
write(*,*)
write(*,"(A16,I3)") ' FLOW ITERATION ',i
if (intarea.ne.zero) then
aux = one/intarea
else
aux = one
end if
write(*,*)
write(*,"(A21,ES14.6)") ' Surface area =',intarea
write(*,"(A21,ES14.6)") ' Mean value of H =',aux*intexp
write(*,"(A21,ES14.6)") ' Mean value of H^2 =',aux*intexp2
write(*,"(A21,ES14.6)") ' ahfdiff/ahfsum =',ahfdiff/ahfsum
if (offset) then
write(*,*)
write(*,"(A6,ES14.6)") ' xc =',xc
write(*,"(A6,ES14.6)") ' yc =',yc
write(*,"(A6,ES14.6)") ' zc =',zc
end if
write(*,*)
write(*,"(A20)") ' Shape coefficients:'
write(*,*)
write(*,"(A4,I2,A3,ES14.6)") ' c0(',0,') =',c0(0)
do l=1+stepz,lmax,1+stepz
write(*,"(A4,I2,A3,ES14.6)") ' c0(',l,') =',c0(l)
end do
end if
if (logfile) then
write(11,*)
write(11,"(A16,I3)") ' FLOW ITERATION ',i
if (intarea.ne.zero) then
aux = one/intarea
else
aux = one
end if
write(11,*)
write(11,"(A21,ES14.6)") ' Surface area =',intarea
write(11,"(A21,ES14.6)") ' Mean value of H =',aux*intexp
write(11,"(A21,ES14.6)") ' Mean value of H^2 =',aux*intexp2
write(11,"(A21,ES14.6)") ' ahfdiff/ahfsum =',ahfdiff/ahfsum
if (offset) then
write(11,*)
write(11,"(A6,ES14.6)") ' xc =',xc
write(11,"(A6,ES14.6)") ' yc =',yc
write(11,"(A6,ES14.6)") ' zc =',zc
end if
write(11,*)
write(11,"(A20)") ' Shape coefficients:'
write(11,*)
write(11,"(A4,I2,A3,ES14.6)") ' c0(',0,') =',c0(0)
do l=1+stepz,lmax,1+stepz
write(11,"(A4,I2,A3,ES14.6)") ' c0(',l,') =',c0(l)
end do
end if
if (nonaxi) then
if (.not.refy) then
if (veryver) then
write(*,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(*,"(A4,I2,A1,I2,A4,ES14.6)") ' cc(',
. l,',',m,') =',cc(l,m)
end if
end do
end do
write(*,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(*,"(A4,I2,A1,I2,A4,ES14.6)") ' cs(',
. l,',',m,') =',cs(l,m)
end if
end do
end do
end if
if (logfile) then
write(11,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(11,"(A4,I2,A1,I2,A4,ES14.6)") ' cc(',
. l,',',m,') =',cc(l,m)
end if
end do
end do
write(11,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(11,"(A4,I2,A1,I2,A4,ES14.6)") ' cs(',
. l,',',m,') =',cs(l,m)
end if
end do
end do
end if
10 format(I4,I4,A2,ES14.6,A1,ES14.6)
else
if (veryver) then
write(*,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(*,"(A4,I2,A1,I2,A4,ES14.6)") ' cc(',
. l,',',m,') =',cc(l,m)
end if
end do
end do
end if
if (logfile) then
write(11,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(11,"(A4,I2,A1,I2,A4,ES14.6)") ' cc(',
. l,',',m,') =',cc(l,m)
end if
end do
end do
end if
20 format(I4,I4,A2,ES14.6)
end if
end if
end if
! Close logfile.
if (logfile.and.(myproc.eq.0)) then
close(11)
end if
! ***********************************
! *** CHECK IF WE HAVE FAILED ***
! ***********************************
! The finder needs a way to give up if there is no
! horizon. At the moment, the way in which I do this
! is that I just give up if the monopole term is of
! the order of 2 grid points in size. Maybe this
! could be improved on?
if (c0(0).lt.2.0D0*dd) then
write(*,*)
write(*,*) 'Surface radius is too small, giving up.'
return
end if
! ********************************************
! *** CHECK IF WE HAVE FOUND A HORIZON ***
! ********************************************
! For this I use a straigthforward test to check if the
! change in the surface is below a given tolerance. This
! usually works well, but if the tolerance is too small then
! the convergence becomes very slow. Also, since I use an
! adaptive stepsize, I run the risk of having a small change
! simply because the stepsize itself is very small, and not
! because we found a horizon. This can happen is the tolerance
! is not small enough. So we have a balancing act here.
if (ahfdiff.lt.ahftol*ahfsum) then
status = .true.
return
end if
end do
! ******************************
! *** TOO MANY IERATIONS ***
! ******************************
! If we ever get here, we did too many iterations and
! failed to converge.
status = .true.
if (veryver) then
write(*,*)
write(*,*) 'Too many iterations'
end if
! ***************
! *** END ***
! ***************
end subroutine AHFinder_flow
|